The sum rules for the spin dependent structure functions $g_1$ in the isovector reaction

Abstract

In the isovector reaction, the sum rule for the spin dependent function $g_1$ which is related to the cross section of the photoproduction is derived. In the small $Q^2$ region, the sum rule is dominated by the low energy contribution and it tightly connects the resonance, the elastic, and the non-resonant contributions.

Comments: Eq.(9) is corrected. The correction is minor and does not affect the disscusion and the conclusion in the paper